Shallow Water Equations With Semi-Submerged Structures Solving a Poisson Equation for the Pressure on the Structure Surface

Abstract

Interaction between currents and semi-submerged structures in coastal areas is a problem of interest in naval and ocean engineering. CFD commercial codes capable of solving these problems have the drawbacks of the high cost of computational resources and time, making them unsuitable for real-time applications in ship maneuvering simulators. This work presents a mathematical model that includes semi-submerged structures in the shallow water equations with hydrostatic assumption. The inclusion of a semi-submerged structure implies the addition of a subdomain with no free surface, replaced by the structure surface. The elevation unknown is replaced by the pressure on the structure surface, which is also unknown. Within this subdomain (for the parcel of fluid under the semi-submerged structure), the 2D-integrated continuity equation is replaced by a Poisson-type equation for the pressure on the structure. This new model is implemented computationally using the finite element method for spatial discretization, and second order schemes for temporal discretization. The results show promising optimization of calculation time per time step, which can lead to the feasibility of real-time applications of hydrodynamic models in ship maneuvering simulators, for example. The numerical results are compared to simulations performed with a CFD commercial code. It shows fairly good agreement in the current magnitude calculations. The elevation and structure surface results are more discrepant, albeit physically realistic. The analysis of CFD results allows concluding that the inclusion of a 3D module and dynamic pressure estimations may improve the results.